This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable.

Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions.

An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.

Originally published by Brooks Cole/Cengage Learning as ISBN: 978-0-534-36224-9.

Graduate students and research mathematicians interested in approximation theory and applications.

Reviews

"Working through this book provides an opportunity to review and apply areas of mathematics learned elsewhere, as well as to learn entirely new topics."

-- MAA Reviews

"The textbook, a clear and concise work written by world-renowned experts in the field of approximation theory, will probe useful not only as a reference for professional mathematicians but also as a text for graduate students."